Direct method for a Cauchy problem with application to a Tokamak

Tadi, M.

doi:10.1016/j.taml.2019.04.002

Cited by 4 publications

(2 citation statements)

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“…We essentially need smooth linearly independent functions that satisfy the periodic boundary condition of the problem. We are using Cubic-B splines, and the details are given in [26].…”

Section: A Direct Methods In Terms Of a Moment Problemmentioning

confidence: 99%

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Non-Iterative Solution Methods for Cauchy Problems for Laplace and Helmholtz Equation in Annulus Domain

Tadi

Radenković

2021

Mathematics

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This note is concerned with two new methods for the solution of a Cauchy problem. The first method is based on homotopy-perturbation approach which leads to solving a series of well-posed boundary value problems. No regularization is needed in this method. Laplace and Helmholtz equations are considered in an annular region. It is also proved that the homotopy solution for the Laplace operator converges to the actual exact solution. The second method is also non-iterative. It is based on the application of the Green’s second identity which leads to a moment problem for the unknown boundary condition. Tikhonov regularization is used to obtain a stable and close approximation of the missing boundary condition. A number of examples are used to study the applicability of the methods with the presence of noise.

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“…We essentially need smooth linearly independent functions that satisfy the periodic boundary condition of the problem. We are using Cubic-B splines, and the details are given in [26].…”

Section: A Direct Methods In Terms Of a Moment Problemmentioning

confidence: 99%

“…The second method is based on the application of Green's identity. We have presented a different approach that uses Green's identity in [26]. Here, we are using point sources to excite the domain, and the formulation is simpler.…”

Section: Introductionmentioning

confidence: 99%